{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T17:03:01Z","timestamp":1784653381791,"version":"3.55.0"},"reference-count":35,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T00:00:00Z","timestamp":1784073600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This manuscript gives a solution to the black hole information paradox by bringing to the debate a fundamental aspect of information science: the process of measurement by a receiver. Bekenstein and Hawking established the foundations of black hole thermodynamics based on previous works of Brillouin and Szilard on information physics. In this work, we demonstrate that the relation between energy and information established in communication technology by Shannon and Landauer has not been adequately applied to black hole physics. As Landauer states, a computation process is closely akin to a measurement. Our argument is grounded on the physical concepts of measurement, signal-to-noise ratio, energy dissipation during the switching process in computation, and hysteresis loops. We give special attention to the role of noise and energy dissipation in the process of information transmission. We demonstrate that Szilard\u2019s work fails to establish a connection between information and entropy in agreement with the works of Landauer and Shannon. We also demonstrate that a quantum state cannot be directly equivalent to a unit of information. The entropy and temperature attributed to black holes are questioned, and a solution to the black hole information paradox is provided. Similarly to what happens with Maxwell\u2019s demon, the black hole information paradox is \u201cexorcised\u201d once we account for the process of measurement and information processing.<\/jats:p>","DOI":"10.3390\/e28070808","type":"journal-article","created":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T08:08:34Z","timestamp":1784189314000},"page":"808","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Measurement Problem in the Thermodynamics of Black Holes"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4525-208X","authenticated-orcid":false,"given":"Jeroen","family":"Schoenmaker","sequence":"first","affiliation":[{"name":"Center for Engineering, Modelling and Applied Social Sciences, Federal University of ABC (UFABC), Santo Andr\u00e9 09280-560, SP, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,7,15]]},"reference":[{"key":"ref_1","unstructured":"Feynman, R., Leighton, R., and Sands, M. (2006). The Feynman Lectures on Physics, the definitive ed., Pearson Addison Wesley."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1038\/248030a0","article-title":"Black hole explosions?","volume":"248","author":"Hawking","year":"1974","journal-title":"Nature"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/BF01645742","article-title":"The Four Laws of Black Hole Mechanics","volume":"31","author":"Bardeen","year":"1973","journal-title":"Commun. Math. Phys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2333","DOI":"10.1103\/PhysRevD.7.2333","article-title":"Black holes and Entropy","volume":"7","author":"Bekenstein","year":"1973","journal-title":"Phys. Rev. D."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A Mathematical Theory of Communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Sys. Tech. J."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Brillouin, L. (1956). Science and Information Theory, Academic Press. [2nd ed.].","DOI":"10.1063\/1.3059856"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1002\/bs.3830090402","article-title":"On the decrease of entropy in a thermodynamic system by the intervention of intelligent beings","volume":"9","author":"Szilard","year":"1964","journal-title":"Behav. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1016\/0042-6989(71)90087-3","article-title":"Visual Recognition of Isolated Lower-Case Letters","volume":"11","author":"Bouma","year":"1971","journal-title":"Vis. Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1147\/rd.53.0183","article-title":"Irreversibility and Heat Generation in the Computing Process","volume":"5","author":"Landauer","year":"1961","journal-title":"IBM J. Res. Dev."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1038\/nature10872","article-title":"Experimental verification of Landauer\u2019s principle linking information and thermodynamics","volume":"483","author":"Arakelyan","year":"2012","journal-title":"Nature"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Schoenmaker, J., Martins, P.G., and Teixeira, J.C. (2025). Temperature Gradients as a Data Storage Principle. Entropy, 27.","DOI":"10.3390\/e27020129"},{"key":"ref_12","unstructured":"Reif, F. (1965). Fundamentals of Statistical and Thermal Physics, McGraw-Hill Book Company."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Rex, A. (2017). Maxwell\u2019s Demon\u2014A Historical Review. Entropy, 19.","DOI":"10.3390\/e19060240"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1016\/S1355-2198(98)00023-9","article-title":"Exorcist XIV: The Wrath of Maxwell\u2019s Demon. Part I. From Maxwell to Szilard","volume":"29","author":"Earman","year":"1998","journal-title":"Stud. Hist. Phil. Mod. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"129273","DOI":"10.1016\/j.physa.2023.129273","article-title":"Ergodic observables in non-ergodic systems: The example of the harmonic chain","volume":"630","author":"Baldovin","year":"2023","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Reichert, P. (2023). The ergodic hypothesis: A typicality statement. arXiv.","DOI":"10.1007\/978-3-031-45434-9_20"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1038\/nphys3518","article-title":"Brownian Carnot engine","volume":"12","author":"Dinis","year":"2016","journal-title":"Nat. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"eadw8462","DOI":"10.1126\/sciadv.adw8462","article-title":"Correlated quantum machines beyond the standard second law","volume":"11","author":"Aguilar","year":"2025","journal-title":"Sci. Adv."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"988","DOI":"10.1038\/nphys1821","article-title":"Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality","volume":"6","author":"Toyabe","year":"2010","journal-title":"Nat. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"13786","DOI":"10.1073\/pnas.1406966111","article-title":"Experimental realization of a Szilard engine with a single electron","volume":"111","author":"Koski","year":"2014","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"911","DOI":"10.1119\/1.2757626","article-title":"The Carnot engine based on the small thermodynamic system: Its efficiency and the ergodic hypothesis","volume":"75","author":"Bormashenko","year":"2007","journal-title":"Am. J. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Bormashenko, E. (2024). Landauer Bound in the Context of Minimal Physical Principles: Meaning, Experimental Verification, Controversies and Perspectives. Entropy, 26.","DOI":"10.20944\/preprints202404.0430.v1"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3077","DOI":"10.1103\/PhysRevD.12.3077","article-title":"Statistical black-hole thermodynamics","volume":"12","author":"Bekenstein","year":"1975","journal-title":"Phys. Rev. D."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1103\/PhysRevD.13.191","article-title":"Black holes and thermodynamics","volume":"13","author":"Hawking","year":"1976","journal-title":"Phys. Rev. D."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"141501","DOI":"10.1103\/PhysRevLett.132.141501","article-title":"Microscopic origin of the entropy of astrophysical black holes","volume":"132","author":"Balasubramanian","year":"2024","journal-title":"Phys. Rev. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1038\/s42254-026-00942-9","article-title":"Black-hole thermodynamics","volume":"8","author":"Mann","year":"2026","journal-title":"Nat. Rev. Phys."},{"key":"ref_27","unstructured":"Ferrari, R.B.V., and Soltau, S.B. (2025). Bekenstein-Hawking Entropy: A Brief Overview. arXiv."},{"key":"ref_28","unstructured":"Cho, A. (2024). Have scientists finally made sense of Hawking\u2019s famous formula for disorder in a black hole?. Science."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"6","DOI":"10.12942\/lrr-2001-6","article-title":"The Thermodynamics of Black Holes","volume":"4","author":"Wald","year":"2001","journal-title":"Living Rev. Relativ."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2015.10.007","article-title":"Black hole remnants and the information loss paradox","volume":"603","author":"Chen","year":"2015","journal-title":"Phys. Rep."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"L149","DOI":"10.1088\/0264-9381\/5\/10\/004","article-title":"On the law of error for mass fluctuation in black holes","volume":"5","author":"Lavenda","year":"1988","journal-title":"Class. Quantum Grav."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"6377","DOI":"10.1063\/1.531249","article-title":"The World as a Hologram","volume":"36","author":"Susskind","year":"1995","journal-title":"J. Math. Phys."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1016\/j.physa.2017.01.052","article-title":"Statistical mechanics of gravitons in a box and the black hole entropy","volume":"473","author":"Viaggiu","year":"2017","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1132","DOI":"10.1038\/nature04804","article-title":"Is our Universe natural?","volume":"440","author":"Carroll","year":"2006","journal-title":"Nature"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"4420","DOI":"10.3390\/e16084420","article-title":"Historical and Physical Account on Entropy and Perspectives on the Second Law of Thermodynamics for Astrophysical and Cosmological Systems","volume":"16","author":"Schoenmaker","year":"2014","journal-title":"Entropy"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/7\/808\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T16:16:45Z","timestamp":1784650605000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/7\/808"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,15]]},"references-count":35,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2026,7]]}},"alternative-id":["e28070808"],"URL":"https:\/\/doi.org\/10.3390\/e28070808","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,15]]}}}